I ended up following this tutorial, creating a new Spring Template Project using the Spring MVC Project template. I then created an EAR (new Enterprise Application Project in Rational Application Developer) that included my new Spring MVC project. Deployed the EAR to my WAS 7, all is fine. I put my CSS and JavaScript files in src/main/webapp/resources and link to them in my views with resources/stylesheet.css. The template project came with a resources directory already set up.

I did notice that its context file referenced http://www.springframework.org/schema/mvc in both the xmlns and the xsi:schemaLocation, not http://www.springframework.org/schema/mvc/spring-mvc as I did in the xsi:schemaLocation, so I think Piotrek's answer is probably correct.